That's sick can have different meanings, so you have to be conscious of the context and the way it's expressed.
1; Can be used to express awe or admiration for something interesting.
2; Can be used to express a disdain for something not-very-pleasant.
Person A: I got a finally got a new phone!
Person B: That's sick! You gonna give me your number?
OR
Person A: And he just gutted the fish! In front of me!
Person B: Ew, that's sick!
Used to describe an action that is perceived as comically undesirable.
Example 1)
Lauren: I accidentally kissed my date on the neck! He was leaning in, so I was in route for a kiss, but apparently he was going for a hug.
Amie: Ewe Laura! You're sick!
Example 2)
Pagina: (Trips and falls, stands up to try to brush it off and does an awkward jig in the process. Doesn't think anyone sees her)
Laurita: Siiick!
Pagina: Chuckles to herself.
To be ill of not feeling well. Sick also means cool, phat, awesome, etc...
Parent: I'm sorry Kelly can make it to school she is sick
Mrs.Claire: I'm sorry to here that I hope she feels better. We will miss her.
1) To be sick- To throw up/puke
2) That's sick!- Cool, insane, crazy, awesome, etc
3) Your behaviour is just sick!- Outrageous, Disgraceful, Horrific
1) "I can't come to school today, i've been sick
2) EMILY: Watch this video, it's amazing!
CAL: OMG, that's sick!
3) "Class 3, your behaviour is sick! You should be ashamed of yourselves!
Another definition for cool.
Person 1: " Did you heard that new Twenty One Pilots song? Its SICK!!?!!!!"
Person 2: " yeah its SO SICK!!!?!!"
Person 1: "SICK!?!?!!!!"
Person 2: "SICK!!!!!!!!!"
A hybrid of the words "sick" and "wicked", but usually only used ironically.